How to translate bump height into real world measurement?
I'd approach it this way:
First, generate a clear black to white gradient image and apply it to a plane as a displacement map.



Then I'd duplicate the plane and apply the displacement modifier, and then check the Z height on the verts that are placed at the black and white parts of the gradeint:



Doing that shows that the black value equals to -0.5 blender units, while the white pixels displace your verts +0.5 blender units.

And then if you want a total white to give you +0.001 bu which is 1mm, all you need to do is to change the dipslacement modifier's stength to 0.002.

Here I used a stength of 0.2 and the resulting height is indeed 0.1 BU:


If your displaced object has a non 1.0 scale value, you'll need to multiply the displacement value by the scale to calculate it. If the scale is non-uniform (let's say 2.0, 1.0, 3.0 for X, Y and Z scale), you're in trouble because it will be different in each axis...